Question

obtain all othere zeroes of the polynomial
$2x ^{3} - 4x - x ^{2} + 2$
if two of its zeroes are
$\sqrt{2}$
and
$\sqrt{2}$


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Answer 1

EXPLANATION.

Two zeroes are = √2 and -√2

zeroes of polynomial.

=> x = √2 and x = -√2

=> x - √2 and x + √2

products of zeroes of polynomial.

=> ( x - √2 ) ( x + √2 )

=> x² - 2

divide 3x³ - 4x - x² + 2 by x² - 2

we get,

=> 2x - 1

Now,

zeroes of the equation

=> 2x - 1 = 0

=> x = 1/2

Therefore,

All zeroes are = 1/2 , √2 , -√2